Which algebraic expression models the word phrase two times the sum of a and b ?
(f) a+b
(g) 2 a+b
(h) 2(a+b)
(i) a+2 b

What is the sum of the finite geometric series?

a. -15+30-60+120-240+480= 315

Given:

a=-15

r= -2

n=6

[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{-15(1-(-2)^{6})}{1+2}\\\\S_6=\frac{-15(1-64)}{3}\\\\S_6=\frac{-15(-63)}{3}\\\\S_6=5*63=315[/tex]

What is a finite geometric series?

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Answer: 1000

Step-by-step explanation:

4000/4

Answer:

1000

Step-by-step explanation:

blank can be written as x. since this is a multiplication problem we need to the opposite of multiplying, which is dividing. rewrite the problem as 4000/4=x

solve by dividing 4000 by 4 to get 1000

Based on the linear pair postulate, the statements and the reasons for the proof are explained below.

The linear pair postulate states that if two angles form a linear pair, then both angles are supplementary, and therefore have a sum of 180 degrees.

The proof that states that angle 1 and angle 3 are congruent angles is shown below:

Statement 1. ∠1 and ∠2 are a linear pair

Reason: Given

Statement 2: ∠1 and ∠2 are supplementary      

Reason: Linear Pair Postulate  

Statement 3: m∠1 + m∠2 = 180°  

Reason: Definition of Supplementary Angles  

Statement 4: ∠2 = ∠4      

Reason: Given  

Statement 5: ∠3 = ∠4

Reason: Vertical Angles Theorem

Statement 6: ∠2 = ∠3

Reason: Corresponding angles theorem  

Statement 7: m∠2 = m∠3

Reason: Corresponding angles are congruent  

Statement 8: m∠1 + m∠3 = 180

Reason: Supplementary angle theorem

Statement 9: <1 and <3 are supplementary

Reason: Definition of supplementary angles

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According to the given data  the property justifies statement is: Multiplication Property of Equality.

According to the Multiplication Property for Equations, an equation can be multiplied as well as divided by the exact number upon every of the equation's sides without changing the solution.

If a = b, then a/c = b/c where c is greater than zero. In other words, if two expressions are equal and subsequently multiply or divide (except for 0) the same constant by both, the two sides will remain equal.

x/2=7

x = 14

Multiplication Property of Equality is :

If a = b,

Multiply constant on both sides.

a * c = b * c

so ,

in the given sum x/2 = 7

multiplying this equation by 2 * x/2 = 7 * 2

                                                                                       = x = 14

According to the given data  the property justifies statement is: Multiplication Property of Equality.

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Answer:

"Games played in a workplace environment to achieve status, advancement and money"

To form a system with an infinite number of solutions, the equation -4x + 6y = 3 must be combined with D. 0.75 + x = 1.5 y.

A system of equations is a set of two or more equations which includes common variables.

To form a system with an infinite number of solutions, the lines should be the same or overlapping. These lines must have the same slope and y-intercept. The equations of these lines must be the multiple of one another.

Given the equation -4x + 6y = 3, rewrite this in the form c + ax = by(same as the form of the choices).

-4x + 6y = 3   ⇒   3 + 4x = 6y

To make 6y into 1.5y, divide both sides by 4.

3 + 4x = 6y   ⇒   0.75 + x = 1.5 y

Hence, the equation -4x + 6y = 3 must be combined with 0.75 + x = 1.5 y to form a system with an infinite number of solutions.

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The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.

We can find the points passing through the lines.

Hence,

The points passing through the line y = x - 11  are:-

Let x = 0

y = -2(0) +1

(0,1)

and;

Let x = 1/2

y = -2(1/2) + 1 = -1 +1

(-1/2,0)

The points passing through the line y = -2x + 16 are:-

Let x = 0

y = -2(0) + 16 =16

(0,16)

and;

Let x = 8

y = -2(8) + 16 = -16 + 16

(8,0)

Hence, using distance formula, the distance between the parallel lines will be:-

[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.

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Answer:

$3,985.00

Step-by-step explanation:

The formula for the amount accrued, A if you invest an amount P at r% compounded annually for n years is given by the formula

[tex]A = P\left(1 + \dfrac{r}{100}\right)^n[/tex][tex]A = P\left(1 + \dfrac{2}{100}\right)^{30} \\\\= P\left(1 + 0.02\right)^{30} \\\\= P\left(1 .02\right)^{30} \\\\= \; \$3,985.00[/tex]

The division by 100 is necessary to allow r% to be reduced to a decimal

So using this formula directly by substituting values gives

Answer:

[tex]4x\left(x-3\right)[/tex]

Step-by-step explanation:

[tex]x^{y+z}=x^yx^z\\x^2=xx\\=4xx-12x\\=4xx-4\cdot \:3x\\=4x\left(x-3\right)[/tex]

The result of multiplying the numbers 234 x 0.35 is 81.9

The numbers are given as:

234 and 0.35

Express the numbers in a product expression

So, we have

234 x 0.35

Express 234 as 200 + 34

So, we have

234 x 0.35 = (200 + 34) x 0.35

Expand the bracket

So, we have

234 x 0.35 = 200 x 0.35 + 34 x 0.35

Evaluate the product

So, we have

234 x 0.35 = 70 + 11.9

Evaluate the sum

So, we have

234 x 0.35 = 81.9

Hence, the result of multiplying the numbers 234 x 0.35 is 81.9

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The components of the two vectors are added and subtracted to produce the addition and subtraction vector PQ. i.e. →PQ = →Q + →P and →PQ = →Q - →P

A vector, which denotes the mathematical and geometrical direction of the provided quantity, is a quantity with both magnitude and direction.

For example : Velocity, Displacement etc.  

Let's start by assuming that,

P(x,y,z) and Q(u,v,w)

Now, we need to find the vector addition and subtraction

Addition of vectors to give →PQ

→PQ = →Q + →P

= (ui + vj + wk ) + (xi + yj + zk)

= (ui + xi ) +(vj  + yj) + (wk +zk)

= (u+x) i + (v + y) j + (w + z)k

= →PQ

Similarly, Subtraction of vectors to give →PQ

→PQ = →Q - →P

= (ui + vj + wk ) - (xi + yj + zk)

= (ui + vj + wk  - xi - yj - zk)

= (ui - xi ) +(vj  - yj) + (wk -zk)

= (u-x) i + (v - y) j + (w - z)k

= →PQ

For example : Let P(1,2,1) and Q ( -1, -2,4)

Then, Addition →PQ = →Q + →P

= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)

=  (1-1) i + (2 -2) j + (1 + 4)k

= oi+0j +5j

= 5j

Subtraction →PQ = →Q - →P

= (1i + 2j + 1k ) - (-1i + (-2)j + 4k)

=  (1+1) i + (2 +2) j + (1 - 4)k

= 2i+4j -3j

Hence, the vector PQ addition and subtraction is given by the addition & subtraction of the components of the two vectors.

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Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

Answer:

A:12.898

B:7.999

Step-by-step explanation:

A: 4.361+8.537

B:2.704+5.295

The area of triangle is 12 square units.

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Given:

The given points are

A=(1,2)

B=(1,8)

C=(5,2)

According to given question we have

By the use of distance formula , we get

[tex]AC=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AC=\sqrt{(5-1)^{2} +(2-2)^{2} }\\\\AC=\sqrt{(4)^{2} +(0)^{2} }\\\\AC=4 units\\\\\\AB=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\AB=\sqrt{(1-1)^{2} +(8-2)^{2} }\\\\AB=\sqrt{(0)^{2} +(6)^{2} }\\\\AB= 6 units[/tex]

Area of right triangle(A) is given by:

[tex]Area =\frac{1}{2} base *height[/tex]

where,

base of the triangle =4 units

height of the triangle =6 units.

[tex]Area =\frac{1}{2} base *height\\\\Area =\frac{1}{2}* 4 *6\\\\Area =12 square units[/tex]

Therefore, the area of triangle is 12 square units.

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Answer:

[tex]y=18x+ 12[/tex]

Step-by-step explanation:

Given equation:

[tex]2+\dfrac{1}{6}y=3x+4[/tex]

Subtract 2 from both sides:

[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]

[tex]\implies \dfrac{1}{6}y=3x+2[/tex]

Multiply both sides by 6:

[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]

[tex]\implies y=18x+ 12[/tex]

Answer:

13

Step-by-step explanation:

first use PEMDAS= P= Parentheses E= Exponents M= Multiplication D= Division A= Addiction S= Subtraction.

(3+6)+6-2=

9+6-2=

15-2=

13

Add 3+6 which is 9

Add 3+6 which is 9then add 9+6 equal to 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15

Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15boom that's how you do it

Answer:

22

Step-by-step explanation:

Use Pemdas

P means parenthesis so add the numbers in the parenthesis

3 + 6 = 9

2(9) + 6 - 2 =

Next is E, but there are no exponents so now there is M

multiply 2 times 9, you will get 18.

18 + 6 - 2 =

So next is A which is addition, add 18 + 6

18 + 6 = 24.

24 - 2

And lastly, S which is subtraction.

24 - 2 = 22

So the answer is 22

When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.

For example :

How many different triangles may be formed with side lengths of 5m,9m and 6 m ?

Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.

We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.

This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed

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Answer:

Solution on Screen

Step-by-step explanation:

It's okay don't worry

Answer:

-0.595

Step-by-step explanation:

..

A quadrilateral (square) may always be used to create a square in a circle. Because squares have right angles at each vertex, every pair of opposing angles in a square is complementary and inscribed in a circle. This is an unavoidable characteristic of squares.

If the form in question is a square, each pair of adjoining angles is supplementary and inscribed in a circle. This is owing to the presence of right angles at each vertex of the square. This means that the assertion can never be proven false.

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Solving for y in terms of x gives y = 31 - 5x

The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.

It is also described as the variable that is being worked out in a given equation.

Given the equation;

5x +y = 31

Let's make 'y' the subject

We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have

y = 31 - 5x

Thus, solving for y in terms of x gives y = 31 - 5x

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The value of f(-4) is 18 because

3(2+4)

6+12=18

Answer:

Step-by-step explanation:

Rate: 54000 brochures per hour

Formula: D=RT   Distance=Rate x Time (In this case distance is the amount)
(I’m not sure if you meant to type 3 1/4 or 314. I’ll include both)
D=54,000(3 1/4)

Two ways

1. 54,000(3 1/4)=175,500

2. 54,000x3 is 162,000, and 1/4 of 54,000 is 54,000/4=13,500. 162,000+13,500=175,500.

(54,000 x 314 = 16,956,000)

Hope this helps!

Answer:

-41

Step-by-step explanation:

h(x) = | 1-7x

First, calculate the value for the function for x = -9

h(-9) = |1--7x|

h(-9) = |1+63|

h(-9) = |64|

h(-9) = 64

23-h(-9) = 23-64 = -41

Hope this helps ;0

The coordinate of the midpoint of JP is -1

On the number line, we have the following coordinates

J = -7

P = 5

The coordinate of the midpoint of JP is calculated using

Midpoint = 1/2 * (J + P)

This gives

Midpoint = 1/2 * (-7 + 5)

Evaluate the sum

Midpoint = 1/2 * -2

Evaluate the product

Midpoint = -1

Hence, the coordinate of the midpoint of JP is -1

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Answer:

20

Step-by-step explanation:

We know that two vertical angles are equal to each other.

Then

First, We have to solve the equation 5y + 10 = 2y + 16  for y.

After that ,we can easily find the measure of the angles by substituting y by its value in their expression.

SOLVING THE EQUATION :

5y + 10 = 2y + 16

⇔ 5y - 2y = 16 - 10

⇔ 3y = 6

⇔ y = 2

Determining the measure of the angles :

angle 1 → 5(2) + 10 = 20

angle 2 → 2(2) + 16 = 20

Answer:

The answer is 36

Step-by-step explanation:

12+6=18

18/3=6

6 squared is 36

36 simplified is still 36

Answer:

Step-by-step explanation:

(i)

[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]

(ii)

[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]

(iii)

[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]

Answer:12+2y

Step-by-step explanation:

Answer:

12 + 2y

Hope this helps :)

Step-by-step explanation:

When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.